The Government wants to know whether there is a relationship between people having an Awareness of Climate Change and Gender. Results from the survey are shown in the cross-tabulation shown below:

	Awareness	Total
Very Aware	Moderately Aware	Little Awareness	No Awareness
Gender	Male	64	44	39	41	188
Female	82	63	37	15	197
Other	6	3	4	2	15
Total	152	110	80	58	400

From the above table, answer the following probability questions, assuming that we randomly select a person from the 400 people in the sample:

1. What is the probability that a person is Very Aware of Climate Change?
2. What is the probability that a person is not Very Aware of Climate Change?
3. What is the probability that a person is Female and Very Aware of Climate Change?
4. What is the probability that a person is Female or Very Aware of Climate Change?
5. What is the probability that a person is Very Aware of Climate Change, given that the person is Female?

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Question 4 (3 points)

A report published in one of the national newspapers recently suggests that 30% of people in Australia have Little or No Awareness of Climate Change. Suppose that 20 people were selected at random.

1. What is the probability that of the 20 residents selected, 4 had Little or No Awareness of Climate Change?
2. What is the probability that of the 20 residents selected, 10 or more had Little or No Awareness of Climate Change?

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Question 5 (3 points)

It is believed that the annual amount spent by households on electricity bills in Australia follows a Normal distribution with a mean () of $1800 and a standard deviation () of $350.

What is the probability that a randomly selected household in Australia will be paying less than $1000 annually? Show your calculations.

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Question 6 (3 points)

Find the probability that a randomly selected customer takes more than 30 seconds to park in a local supermarket car park. We know that the time taken for a customer to find a vacant car spot has an exponential distribution with a mean of 2 minutes. Show your calculations.

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